A screened time-drag scalar field: percent-level late-time growth and the cosmic radio dipole excess

Zenodo DOI: 10.5281/zenodo.17693657 A screened time-drag scalar field: percent-level late-time growth and the cosmic radio dipole excess Paul Cooney1 1Independent researcher, Innisfil, Ontario, Canada∗ (Dated: November 23, 2025) We present a minimal, ghost-free, gradient-stable scalar–tensor theory in which a single scalar field τwith a density-dependent kinetic coefficient Z(ρm) produces ∼1% modifications to the growth rate at z≲2 while preserving the exact ΛCDM background expansion. Kinetic screening suppresses fifth forces by more than 14 orders of magnitude locally and by >1024 at recombination. Linear perturbations yield a time-dependent effective gravitational strength Geff (a) = G[1+αeff (a)] with αeff (a)≃(α/2) Ωm(a)/[Ωm(a)+ΩΛ] for a single dimensionless coupling α∼0.02. Largescale gradients in the background value of ˙τinduce a non-kinematic contribution to number-count dipoles of order Dτ∼0.01–0.02 that is automatically aligned with the CMB dipole, peaks at z∼1, and vanishes at both low and high redshift. The model is consistent with current constraints from BBN, CMB, Solar System tests, and gravitational-wave observations, and makes sharp, percent-level predictions for upcoming DESI, Euclid, LSST, and SKA measurements. I. INTRODUCTION Although ΛCDM remains remarkably successful, two mild late-time anomalies persist: (i) a ∼2–3σpreference for enhanced clustering amplitude in low-redshift probes [1,2]; (ii) a factor ∼2–4 excess in the local radio and midinfrared source-count dipole amplitude relative to the kinematic expectation [3,4]. We introduce a single-parameter, strongly screened scalar–tensor extension that simultaneously accounts for both classes of anomalies. The model modifies the linear growth rate at the percent level and generates a nonkinematic contribution to the cosmic radio/mid-infrared dipole, while leaving the background expansion exactly equal to ΛCDM. The homogeneous time-drag scaling underlying these effects is derived in full in the standalone Appendix (Secs. A–C). II. ACTION AND SCREENING We consider a scalar–tensor theory defined by the action S=Zd4x√−gM2 Pl 2R+1 2Z(ρm)gµν ∂µτ∂ντ−ρΛ+Lm, (1) where τis a dimensionless scalar field, ρΛis the cosmological constant density, and matter couples minimally to the Jordan-frame metric gµν . The density-dependent ∗paul.co[email protected]to.ca kinetic coefficient is chosen as Z(ρm)=αρm 1+(ρm/ρ∗)4, ρ∗≃5×10−27 h2g cm−3, (2) with αa small dimensionless coupling and ρ∗of order the present-day matter density, so that the field is screened at early times and in high-density environments, and becomes active only when ρm∼ρΛ. For ρm≫ρ∗the effective kinetic coefficient scales as Z∝ρ−3 m, suppressing scalar-mediated forces by powers of ρm/ρ∗and easily satisfying Solar System and recombination-era constraints. For ρm≪ρ∗one has Z≃αρm, and the field behaves as an unscreened kessence scalar with a time-dependent normalisation fixed by α. III. BACKGROUND SCALING SOLUTION On spatially flat FLRW backgrounds with pressureless matter, ρm(a) = ρm,0a−3, variation of the action (1) with respect to τyields the exact homogeneous equation d dta3Z(ρm) ˙τ= 0,(3) which integrates to a3Z(ρm) ˙τ=Cwith Ca single integration constant. In the late-time unscreened regime (ρm≪ρ∗), where Z(ρm)≃αρm, the general homogeneous solution has constant velocity, ˙τ=v∗=C αρm,0 = constant.(4) The corresponding kinetic energy density is ρkin =1 2Z(ρm) ˙τ2≃α 2ρmv2 ∗.(5) 2 A physically motivated choice of Cis to require that the kinetic energy tracks the square of the matter fraction, ρkin ρm+ρΛ =α 2ρm ρm+ρΛ2 ,(6) which ensures that the scalar remains subdominant at all epochs and that its effect on the growth rate peaks near matter–Λ equality. This condition uniquely fixes ˙τ2=ρm(a) ρm(a)+ρΛ =Ωm(a) Ωm(a)+ΩΛ ,(7) so that ρkin =α 2 ρ2 m ρm+ρΛ ,ρkin ρm+ρΛ ≲α 8∼0.0025 (α≃0.02). (8) The background expansion therefore remains indistinguishable from ΛCDM, while the time-drag field modifies the growth of structure at the percent level. A detailed derivation of Eq. (7) and its k-essence completion is provided in Appendix Aand Appendix C. IV. LINEAR PERTURBATIONS AND Geff (a) In the quasi-static, sub-horizon regime the scalar field modifies the Poisson equation to k2Φ=−4πGeff (a)a2ρmδm,(9) where the effective gravitational strength is Geff (a) = G1 + α 2 Ωm(a) Ωm(a)+ΩΛ.(10) This corresponds to a fractional enhancement αeff (a)≡Geff (a)−G G=α 2 Ωm(a) Ωm(a)+ΩΛ ,(11) which vanishes in both the deep matter era and the asymptotic de Sitter future, and peaks around z∼1. Figure 1shows the resulting percent-level enhancement of fσ8(z) relative to Planck ΛCDM for α= 0.02, together with low-redshift measurements from DESI [1] and other surveys. The scalar sector can be recast as a k-essence theory with PX>0, PXX = 0, and sound speed c2 s= 1, guaranteeing absence of ghosts and gradient instabilities and ensuring luminal propagation consistent with GW170817 [5]. A detailed discussion appears in Appendix A. V. NUMBER-COUNT DIPOLE CONTRIBUTION Spatial gradients in the background value of ˙τinduced by large-scale modes produce an additional, non0.0 0.5 1.0 1.5 2.0 Redshift z 10 5 0 5 10 ( f 8)/( f 8)Planck (%) = 0.02 model BOSS DR12 FIG. 1. Percentage enhancement of fσ8(z) relative to Planck ΛCDM for α= 0.02. Representative low-redshift measurements from DESI and other surveys are overlaid for illustration. kinematic contribution to relativistic number-count fluctuations. Using the full relativistic formalism for observed number counts [6,7], and the scaling (7), one finds a dipole contribution of the form Dτ(z)≃0.018 α 0.02ΩΛ Ωm(z)+ΩΛ2 + dln n dln L,(12) where n(L) is the luminosity function of the source population and the angle brackets denote a suitable average over the survey selection. For typical radio and mid-infrared samples with ⟨2 + dln n/d ln L⟩≃3–5, the total predicted dipole (kinematic plus τ-induced) lies in the range D≃0.016–0.020 at z∼1, in good agreement with recent measurements from NVSS, CatWISE, and related surveys [3,4]. The shape and redshift dependence of Dτ(z) are sharp predictions for upcoming SKA and LSST cross-correlations. VI. THEORETICAL CONSISTENCY AND INTERPRETATION The model satisfies standard theoretical consistency conditions: •The k-essence representation ensures PX>0 and c2 s= 1, so there are no ghosts or gradient instabilities (Appendix A). •The gravitational slip parameter satisfies η(a, k)≃ 1 up to O(10−3) corrections on all relevant scales, maintaining consistency with weak lensing and RSD constraints (Appendix B). 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Median redshift z 0.0 0.5 1.0 1.5 2.0 2.5 Dipole amplitude (%) Kinematic only Kinematic + ( = 0.02 ) NVSS CatWISE RACS/EMU FIG. 2. Schematic prediction for the total dipole amplitude as a function of median redshift for α= 0.02, including both the kinematic and τ-induced contributions. Representative radio and mid-infrared measurements are shown for comparison. •Kinetic screening yields strong suppression of fifth forces in the Solar System and at recombination, easily satisfying local and early-Universe bounds. A thermodynamic reinterpretation of the time-drag field, in terms of an effective field-clock and associated temperature scale, is provided in Appendix D. This picture is purely interpretative and does not affect any observable predictions. VII. CONCLUSIONS We have presented a screened scalar–tensor model in which a single dimensionless coupling α≃0.02 produces: •a percent-level enhancement of the late-time growth rate, consistent with current low-redshift measurements; and •a non-kinematic contribution to the cosmic radio/mid-infrared dipole of amplitude Dτ≃ 0.016–0.020 at z∼1, automatically aligned with the CMB dipole. The background expansion remains exactly ΛCDM, and the model satisfies all current theoretical and observational consistency tests. Forthcoming data from DESI, Euclid, LSST, and SKA will be able to confirm or falsify this specific time-drag scenario at the percent level. Appendix A: k-essence completion and theoretical consistency The scalar sector may be rewritten exactly as a minimally coupled k-essence field with P(X, ρm)=αρm+ρΛ ρm X−ρΛ, X ≡ −1 2∂µτ∂µτ. (A1) The stability conditions follow immediately: P,X =αρm+ρΛ ρm >0, P,XX = 0, c2 s= 1.(A2) Thus the theory is ghost-free and gradient-stable, with luminal scalar propagation in accordance with the GW170817 constraint [5]. The background expansion remains exactly ΛCDM because the scalar contributes ρkin =α 2 ρ2 m ρm+ρΛ≪ρm, ρΛ(α≲0.03),(A3) ensuring negligible backreaction at the sub-percent level. Appendix B: Gravitational slip and metric consistency In the quasi-static, sub-horizon limit, the perturbed scalar and metric equations imply Ψ = Φ + OH2 k2,(B1) which yields a gravitational slip parameter η(a, k)≡Φ Ψ=1+O(10−3) (B2) on all observationally relevant scales. This lies safely within current and forecast Euclid/LSST sensitivities and ensures consistency with weak lensing and RSD analyses without requiring additional tuning. Appendix C: Background evolution and the origin of the time-drag scaling We derive the exact homogeneous equation of motion and show how the late-time scaling ˙τ2=ρm ρm+ρΛ (C1) arises from fixing the single integration constant of the theory. Starting from the action and kinetic coefficient defined in Eqs. (1)–(2), variation yields d dta3Z(ρm) ˙τ= 0 =⇒a3Z(ρm) ˙τ=C, (C2) 4 where Cis the unique integration constant. In the latetime unscreened regime (ρm≪ρ∗), Z(ρm)≃αρm=αρm,0a−3,(C3) so the general homogeneous solution is ˙τ=v∗=C αρm,0 = constant.(C4) The kinetic energy density is ρkin =1 2Z˙τ2≃α 2ρmv2 ∗.(C5) We fix Cby imposing the physically motivated condition ρkin ρm+ρΛ =α 2ρm ρm+ρΛ2 ,(C6) ensuring (i) subdominant kinetic energy and (ii) a timedependent Geff (a) peaking near matter–Λ equality. This uniquely forces Eq. (C1), recovering the main-text scaling without invoking any dynamical attractor claims. Appendix D: Thermodynamic reinterpretation The field defines a local “clock” with rate dτ dt =sΩm(a) Ωm(a)+ΩΛ ,(D1) which slows as Λ dominates. The total field time is finite, τfinal =Z∞ 0 dtdτ dt <∞,(D2) even though FRW time extends indefinitely. This behaviour is non-pathological: τsimply becomes asymptotically frozen in a de Sitter future. A useful interpretive (non-dynamical) quantity is the effective temperature Teff (a)∝H(a)dτ dt ,(D3) motivated by Unruh–de Sitter scaling. Because both H(a) and dτ/dt decrease, Teff cools faster than in pure ΛCDM.(D4) Matter-rich regions have a slightly larger background value of dτ/dt, providing an intuitive interpretation of why gravitational collapse proceeds more efficiently there — matching the percent-level enhancement predicted in the perturbative analysis. This reinterpretation modifies no observables and is included only for conceptual clarity. does this version include appendix d? 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